Robust RRE technique for increasing the order of accuracy of SPH numerical solutions

This study presents the use of a post-processing technique called repeated Richardson extrapolation (RRE) to improve the accuracy of numerical solutions of local and global variables obtained using the smoothed particle hydrodynamics (SPH) method. The investigation focuses on both the steady and unsteady one-dimensional heat conduction problems with Dirichlet boundary conditions, but this technique is applicable to multidimensional and other mathematical models. By using all the variables of the real type and quadruple precision (extended precision or Real*16) we were able to, for example, reduce the discretization error from 1.67E−08 to 3.46E−33 with four extrapolations, limited only by the round-off error and, consequently, determining benchmark solutions for the variable of interest ψ(1/2) using the SPH method. The increase in CPU time and memory usage owing to post-processing was almost null. RRE has proven to be robust in determining up to a sixteenth order of accuracy in meshless discretization for the spatial domain.